Active Positive-Definite Matrix Completion
نویسندگان
چکیده
In the FindCandidates function (line 4), Select finds all the single edges that can be added to the current mask graph GΩ while maintaining its chordal structure. To do that, we make use of the clique tree data structure as introduced by Ibarra [1]. Given a graph G = (V,E), the clique tree is a tree C = (VC , EC), in which each node is a maximal clique of G, i.e., VC ⊂ 2 . In our case the number of nodes |VC | is O(n) because G is chordal [1]. Two cliques are connected in the clique tree if they share common nodes. According to Ibarra, retrieving the insertable edges e = (i, ·), i.e., those that are attached to node i ∈ V , requires running a depthfirst search on C (line 4). For every clique c ∈ VC that we visit and for each node j ∈ c, we check if the edge (i, j) is insertable. As a result, it takes O(n) time to retrieve the set of all insertable edges. The pseudocode of this procedure is summarized in Algorithm 3.
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